GM of the numbers $3, 3^{2}, 3^{3}, . . . . ., 3^{n}$ is.

3^{2 / n}

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3^{n / 2}

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3^{(n + 1) / 2}

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3^{(n - 1) / 2}

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Solution

The correct option is C $3^{(n + 1) / 2}$
GM of the numbers $3, 3^{2}, 3^{3}, . . . . ., 3^{n}$ is
$= (3^{1} \times 3^{2} \times 3^{3} \times . . . . . . . . . . \times 3^{n})^{\frac{1}{n}}$
$= (3^{1 + 2 + 3 + . . . . . . . . . . + n})^{\frac{1}{n}}$ $= 3^{\frac{n (n + 1)}{2} \times \frac{1}{n}} = 3^{\frac{n + 1}{2}}$
Hence, option 'C' is correct.

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